Hello, I only want to give thank you to all users of this forum, because all those people helped me a lot and I expect that they will help me in future as well.
To the MMF is a really helpful forum to me and maybe it is the finest forum of the universe till now.
Here is some thoughts I'd like to share:

The favourite moderators of mine: The Chaz, CRGreathouse
The most useful moderators of MMF: MarkFL, greg1313
The most favourite jokers of mine: ZardoZ, Soroban
The masters of convergency: Dougy, CRGreathouse.
The masters of diophantine equation: brangelito
The masters of complex analysis: ZardoZ, galactus

Thank you all
Sorry, maybe I cannot visit this forum for atleast 9 days, its because of my exam, but I think this dosent matters(as i told before, ¾ of my post is junk)

One day -- not any time soon -- I hope to join their ranks. I'd love to learn complex analysis and the circle method but I just haven't managed so far. (I took a basic course in complex analysis, through Little Picard, but I'd need at least three times that to get comfortable with the subject.)

One day -- not any time soon -- I hope to join their ranks. I'd love to learn complex analysis and the circle method but I just haven't managed so far. (I took a basic course in complex analysis, through Little Picard, but I'd need at least three times that to get comfortable with the subject.)

Hey, every day that I come by here I get to add a whole new wing to my universe of "conscious incompetence", ie I become aware of yet another whole area of study that I didn't even know existed that I now know does, but that I know all but nothing about! It leaves one "feeling small beneath the stars" indeed!

And yet, progress proceeds on several fronts. What more can one ask?

As for complex analysis, I haven't even dared glance at the forum yet!

Hey, every day that I come by here I get to add a whole new wing to my universe of "conscious incompetence", ie I become aware of yet another whole area of study that I didn't even know existed that I now know does, but that I know all but nothing about! It leaves one "feeling small beneath the stars" indeed!

It almost screams for more questions. At what point did you feel you knew the smallest percentage of all of math? The largest? And at what point did you feel you lacked the largest total amount of math?

The last answer for me is always "right now": I always find out about new math faster than I learn it. The others seem to have fixed answers: end of high school (felt like I knew a lot, but didn't yet know how much was out there) and ~junior year in college (eyes finally opened to the amount of math 'out there', hadn't really learned any of it yet).

As for complex analysis, I haven't even dared glance at the forum yet!

Let me give my mini-overview of the subject. Analysis is, of course, just the mathematical name for what high-school students call Calculus -- the simple parts get called calc and the hard parts analysis. It's split into two branches: real and complex. Real analysis is just what it sounds like. Complex analysis sounds like it should be harder: instead of the usual 1-dimensional real numbers, you're using the two-dimensional complex numbers (so even a graph is 4-D, too large to plot). But in fact it's just the opposite. Real analysis works with the nastiest, most complicated functions you can dream up, where complex analysis is really the study of analytic functions (and various extensions like meromorphic functions), the nicest possible functions you could hope for. So real analysis looks back at calculus and says, "what are the worst possible cases, and how can we handle those?", where complex analysis says, "what are the nicest things, and how could we make them nicer by studying them in a larger realm?".

As for complex analysis, I haven't even dared glance at the forum yet!

Let me give my mini-overview of the subject. Analysis is, of course, just the mathematical name for what high-school students call Calculus -- the simple parts get called calc and the hard parts analysis. It's split into two branches: real and complex. Real analysis is just what it sounds like. Complex analysis sounds like it should be harder: instead of the usual 1-dimensional real numbers, you're using the two-dimensional complex numbers (so even a graph is 4-D, too large to plot). But in fact it's just the opposite. Real analysis works with the nastiest, most complicated functions you can dream up, where complex analysis is really the study of analytic functions (and various extensions like meromorphic functions), the nicest possible functions you could hope for. So real analysis looks back at calculus and says, "what are the worst possible cases, and how can we handle those?", where complex analysis says, "what are the nicest things, and how could we make them nicer by studying them in a larger realm?".

As for complex analysis, I haven't even dared glance at the forum yet!

Let me give my mini-overview of the subject. Analysis is, of course, just the mathematical name for what high-school students call Calculus -- the simple parts get called calc and the hard parts analysis. It's split into two branches: real and complex. Real analysis is just what it sounds like. Complex analysis sounds like it should be harder: instead of the usual 1-dimensional real numbers, you're using the two-dimensional complex numbers (so even a graph is 4-D, too large to plot). But in fact it's just the opposite. Real analysis works with the nastiest, most complicated functions you can dream up, where complex analysis is really the study of analytic functions (and various extensions like meromorphic functions), the nicest possible functions you could hope for. So real analysis looks back at calculus and says, "what are the worst possible cases, and how can we handle those?", where complex analysis says, "what are the nicest things, and how could we make them nicer by studying them in a larger realm?".

Oh, ok! That's heartening! I'll work up the nerve to start lurking there soon, then!

And as for the matter of the growth rate of the awareness of the vastness of one's ignorance far exceeding the growth rate of actual knowledge, there are times when it makes me absolutely dizzy, but since I realize that it's the very nature of the pursuit of knowledge that new questions pop up faster than old ones are answered, I just end up strapping myself in to enjoy the ride! I had a linguistics professor named Eric Hamp whose knowledge of language in general and historical linguistics (esp Indo_Eurpoean) was nothing less than encyclopedic, and he had the endearing habit of answering questions whose answers he did NOT know with "Sorry, but there aren't enough gaps in my ignorance to answer that!" Another genuinely genius level professor of mine, James McCawley, would end discussions of complex and/or controversial matters with "I've already told you more than I know about this." When I would come to McCawley with something novel I was working on, I would often ask him what the conventional wisdom was on the puzzle I was attacking and he on a few occasions said: There's not only no conventional wisdom, there's no conventional BS on THAT topic! Jim had a definition of 'red herring' that went "something you don't believe but teach to your students anyway". So what he was saying was that there weren't even any red herrings in his sense on the topic. And I was not particularly prone to go looking terribly far afield for issues to address. The questions I tended to asked seemed pretty obvious to me. So the fact that this was his response on more than just one or two occasions was an object lesson in how little is really known even collectively. We will never ever run out of new questions.